Answer:
(1 cm)cos3πt
Step-by-step explanation:
Since the piston starts at its maximal height and returns to its maximal height three times evert 2 seconds, it is modelled by a cosine functions, since a cosine function starts at its maximum point. So, its height h = Acos2πft
where A = amplitude of the oscillation and f = frequency of oscillation and t = time of propagation of oscillation.
Now, since the piston rises in such a way that it returns to the maximal height three times every two seconds, its frequency, f = number of oscillations/time taken for oscillation where number of oscillations = 3 and time taken for oscillations = 2 s
So, f = 3/2 s =1.5 /s = 1.5 Hz
Also, since the the piston moves between 3 cm and 5 cm, the distance between its maximum displacement(crest) of 5 cm and minimum displacement(trough) of 3 cm is H = 5 cm - 3 cm = 2 cm. So its amplitude, A = H/2 = 2 cm/2 = 1 cm
h = Acos2πft
= (1 cm)cos2π(1.5Hz)t
= (1 cm)cos3πt
Answer:
12x^6y
Step-by-step explanation:
Check the picture below.
notice that the car exits the northbound highway, and whilst going at 50mph for 1.5 hours, that simply means going for 75 miles.
make sure your calculator is in Degree mode.
Answer:
Cost of One Journal = $3.99
Cost of One pen = $0.59
Step-by-step explanation:
Let
Cost of One Journal = x
Cost of One pen = y
We can make equation from given statements.
Mr. Bowden purchases 18 journals and 40 pencils for $95.42.
![18x+40y=95.42](https://tex.z-dn.net/?f=18x%2B40y%3D95.42)
Ms. Jacinto purchases 11 journals and 16 pencils for $53.33.
![11x+16y=53.33](https://tex.z-dn.net/?f=11x%2B16y%3D53.33)
Now solving these equations to find the value of x
![18x+40y=95.42--eq(1)\\11x+16y=53.33--eq(2)](https://tex.z-dn.net/?f=18x%2B40y%3D95.42--eq%281%29%5C%5C11x%2B16y%3D53.33--eq%282%29)
Multiply eq(1) with 2 and eq(2) with 5
![36x+80y=190.84\\55x+80y=266.65\\-\:\:\:\:-\:\:\:\;\:\:\:\:\:\:\:-\\---------\\-19x=-75.81\\x=\frac{-75.81}{-19}\\x=3.99\\](https://tex.z-dn.net/?f=36x%2B80y%3D190.84%5C%5C55x%2B80y%3D266.65%5C%5C-%5C%3A%5C%3A%5C%3A%5C%3A-%5C%3A%5C%3A%5C%3A%5C%3B%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A%5C%3A-%5C%5C---------%5C%5C-19x%3D-75.81%5C%5Cx%3D%5Cfrac%7B-75.81%7D%7B-19%7D%5C%5Cx%3D3.99%5C%5C)
We get the value of x is: x=3.99
Now, putting value of x in equation 1 to find value of y.
![18x+40y=95.42\\18(3.99)+40y=95.42\\71.82+40y=95.42\\40y=95.42-71.82\\40y=23.6\\y=\frac{23.6}{40}\\y= 0.59](https://tex.z-dn.net/?f=18x%2B40y%3D95.42%5C%5C18%283.99%29%2B40y%3D95.42%5C%5C71.82%2B40y%3D95.42%5C%5C40y%3D95.42-71.82%5C%5C40y%3D23.6%5C%5Cy%3D%5Cfrac%7B23.6%7D%7B40%7D%5C%5Cy%3D%200.59)
So, we get the value of y: y = 0.59
Now, finding the costs:
Cost of One Journal = x = $3.99
Cost of One pen = y = $0.59